Singular value decomposition is a factorization of a matrix A taking the following form: A=USV*, where U is an m-by-m unitary matrix, S is an m-by-n rectangular diagonal matrix (where “m” and “n” are positive integers), and V* (the conjugate transpose of V) is an n-by-n unitary matrix. The diagonal entries of S are non-negative real values referred to as the “singular values” of the matrix A.
In the most general form, the elements of matrix may be real, imaginary (some multiple of √{square root over (−1)} symbolically represented as i) or complex numbers (a sum of real and imaginary numbers). A real matrix is a matrix that includes only real numbers as elements. A complex matrix is a matrix that may include elements that are real numbers, but also includes at least one element that is imaginary or complex.
There are a wide variety of software applications that can reliable perform singular value decomposition of a real matrix, but yet cannot perform singular value decomposition of a complex matrix.